Actually, I think as an American I can shed some light on the subject, and it is not necessarily grammar related.
"Discretion" in this instance is a synonym for judgment, reason, as in, "Decide at your own discretion." Usually, when a play, a film, or (most commonly) a television show is presented, the creators of the show feel obligated, morally and in some cases legally, to make a summary of the content of what the viewer is about to see. There is little the government can do to censor the writers and actors if they want to include violent or heavily sexual content: this is part and parcel to creating art and otherwise so long as it is not off-the-charts graphic that it may make audiences flee in terror or disgust to the streets, all is well. (Equally there is not much it can do if the village idiot decides The Human Centipede is good family fun, but that is a whole other story.)
On the other hand, there is the issue of children. There are programs on television, plays, video games, and films in theatres that are just not suitable for a little one to watch: a little fellow needs his innocence to be preserved and it is not right to expose him to something that may not be intended for his enjoyment (not the target audience) or he is just emotionally or cognitively not ready to handle. Though the writers and actors cannot be held responsible for a parent's negligence (children are presumed to be their parents' responsibility in American law and society) they can be held responsible for not putting forth a warning.
There have been bad screw-ups in the past. For example, a lot of Spielberg's films from the 1980s were acceptable under the PG rating even though today they are not recommended as such-what happened? Answer: when he released Poltergeist, which had the PG rating, and later Indiana Jones and the Temple of Doom, also PG, parents assumed that these would be okay to bring their seven year olds to see; they had little reason to believe it wouldn't be too scary for the kids as Spielberg was riding high for making E.T. at the time. Unfortunately parents and children got the unpleasant surprise of witnessing a 5 year old girl being stolen from her family and getting sucked into a closet, and in the case of Indiana Jones, a man getting his heart cut out before being lowered into a fiery pit as a human sacrifice. Of course, it resulted in many children terrified of turning the lights out or screaming and bawling their little eyes out every time they heard the Indiana Jones Overture.
The pattern repeated itself later on television with some shows like Cops and Beavis and Butthead and later still with video games like Mortal Kombat and Doom. So better ratings systems and fair warning in the form of disclaimers like "viewer discretion is advised" became the compromise position between allowing the writers, animators, producers, and actors freedom of expression, and at the same time protecting the children from content that might not be good for them until they are older.